A simple solenoid consists of a coil and a plunger. When one end of the plunger is placed in or near the end of the coil, it becomes magnetized, and mutual attraction results between the flux in the plunger and the magnetic force due to the ampere-turns in the winding of the solenoid. The plunger becomes more and more saturated as it enters the solenoid. The pull on the plunger drops to zero when the plunger is magnetically centered in the solenoid. The pulling force of a solenoid can be greatly enhanced by enclosing the coil in a frame of magnetic material. This adds an additional component to the pulling force of the solenoid, namely, the pull between the frame and the end of the plunger. As the air gap between the end of the plunger and the frame decreases, the latter component becomes predominant and the pulling force as a function of the deflection of the plunger rises rapidly as the gap approaches zero. While the addition of the frame of magnetic material greatly increases the force at which the solenoid "locks in", it does not improve the performance of the solenoid over an extended range of movement. This has only been accomplished in the past by increasing the component of force produced by the solenoid action between the coil and the plunger, namely, by increasing the ampere-turns of the coil or other parameters, such as the cross-sectional area of the plunger, the proportions of the coil, and the degree of saturation and length of the plunger.